The operators and functions which construct a subgroup of a polycyclic group always return the subgroup as a polycyclic group.
Construct the conjugate g - 1 * H * g of the group H under the action of the element g. The group H and the element g must belong to a common group.
Given a subgroup H of the group G, construct the normal closure of H in G.
Construct the commutator subgroup of groups H and K, where H and K are subgroups of a common group G.
The operators and functions described in this section require the existence of a nilpotent covering group. They are based on algorithms published in [Lo98]. Again, the constructed subgroup is returned as a polycyclic group.
Given two groups H and K, contained in some common group G which is nilpotent, construct the intersection of H and K.
Given two groups H and K, contained in some common group G which is nilpotent, replace H with the intersection of H and K.
The subgroup of G centralising g. Both g and G must be contained in some common nilpotent group.
The subgroup of G centralising H. Both H and G must be subgroups of some common nilpotent group.
The maximal normal subgroup of the nilpotent group G that is contained in the subgroup H of G.
The subgroup of G normalising H. Both H and G must be subgroups of some common nilpotent group.